Special Session 22: Modeling and dynamic analysis of complex patterns in biological systems and data
Contents
In this talk I will discuss joint work with Lake Ritter and Jay Walton on modeling inflammatory instability in coupled in the lumen and subendothelia layer system. First we will introduce a steady state equilibrium in the lumen which will generate non-standard condition on the interface between lumen and subendothelia. Nest we will investigate structural stability of linearized system depending on the input parameters and boundary conditions.
The notion of a "healthy state" is then introduced as an equilibrium state in which inflammatory markers are absent. The mathematical question studied is the stability of this healthy state to small perturbations in the inflammatory markers. It is shown that the healthy state can be stabilized through hydro-diffusion processes and sufficiently strong anti-oxidant mitigation and destabilized through strong chemotactic and hydrodynamic effects which promote local lesion formation and growth and low anti-oxidant levels.